BGV API

Data Structures

Poseidon Supported parameter data structures, the following is specific to BGV：


1. BGV encoding and decoding class : BatchEncoder

Description：BatchEncoder is used to encode and decode message in the BGV encryption scheme.

Functions：

BatchEncoder(const PoseidonContext &context);
  • context (const PoseidonContext &): The poseidon context.

Usage: Construction function creates a BatchEncoder. It is necessary that the encryption parameters given through the PoseidonContext object support batching.

void encode(const vector<uint32_t> &src, Plaintext &plain);
  • src (const vector &): The source message.
  • plain (Plaintext &): The source message.

Usage: A function used to encode a vector of integer into a plaintext.

void decode(const Plaintext &plain,vector<uint32_t> &res);
  • plain (const Plaintext &plain): The plaintext.
  • res (vector &): The result message.

Usage: A function used to decode a plaintext into a vector of integer.


2. Plaintext matrix class : MatrixPlain

Description: MatrixPlain is a class for storing plaintext matrix.

  • Description: MatrixPlain is a class for storing plaintext matrix information.

c++ MatrixPlain() : log_slots(0), n1(0), level(0), scale(1.0), rot_index{}, plain_vec_pool{sz, std::map<int, Plaintext>()}, read_idx(0), write_idx(0), is_precompute(false)

Members:

  • LogSlots (uint32_t): Indicates the logarithm to 2 of the number of matrix elements.

  • N1 (uint32_t): Indicates the number of rows in a matrix.

  • level (uint32_t): Indicates the level of the ciphertext module chain in which the matrix resides.

  • scale (double): Indicates the scaling factor of the matrix.

  • rot_index (vector):Indicates the rotation index of a matrix element in a polynomial.

  • plain_vec (map):Indicates the polynomial corresponding to the matrix elements.

  • plain_vec (map):Indicates the polynomial corresponding to the matrix elements.


3. Evaluator class : EvaluatorBgvBase

Description: EvaluatorBgvBase is a evaluator for homomorphic computation for BGV scheme.

Members: The member functions are listed in Chapter Evaluation Functions.


Evaluation Functions

1. Addition between ciphertexts : add

void add(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result) const;

Description：This function performs homomorphic addition on two ciphertexts.

  • ciph1 (Ciphertext): representing a ciphertext.
  • ciph2 (Ciphertext): representing another ciphertext.
  • result (Ciphertext): storing the computation result.

Usage: add computes result = ciph1 + ciph2 .


2. Addition of ciphertext and plaintext : add_plain

void add_plain(const Ciphertext &ciph, const Plaintext &plain, Ciphertext &result) const;
  • ciph (Ciphertext): representing a ciphertext.
  • plain (Plaintext): representing a plaintext.
  • result (Ciphertext): storing the computation result.

Usage: add_plain computes result = ciph + plain .


3. Ciphertext and ciphertext subtraction : sub

void sub(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result) const;
  • ciph1 (Ciphertext): representing the minuend (the number from which another is to be subtracted).
  • ciph2 (Ciphertext): representing the subtrahend (the number to be subtracted).
  • result (Ciphertext): storing the computation result.

Usage: sub computes result = ciph1 - ciph2.


4. Subtraction plaintext from ciphertext : sub_plain

void sub_plain(const Ciphertext &ciph, const Plaintext &plain, Ciphertext &result) const;
  • ciph (Ciphertext): representing the minuend (the number from which another is to be subtracted).
  • plain (Plaintext): representing the subtrahend (the number to be subtracted).
  • result (Ciphertext): storing the computation result.
  • Usage: sub_plain computes result = ciph - plain .


5. Multiplication between ciphertexts : multiply ( only software)

void multiply(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result) const;
  • ciph1 (Ciphertext): representing a ciphertext.
  • ciph2 (Ciphertext): representing another ciphertext.
  • result (Ciphertext): storing the computation result.

Usage: multiply computes result = ciph1 * ciph2.


6. Multiplication between ciphertext and plaintext : multiply_plain

void multiply_plain(const Ciphertext &ciph, const Plaintext &plain, Ciphertext &result) const;
  • ciph (Ciphertext): representing a ciphertext.
  • plain (Plaintext): representing a plaintext.
  • result (Ciphertext): storing the multiplication result.

Usage: multiply_plain computes result = ciph * plain.


7. Multiplication with relinearization : multiply_relin

void multiply_relin(const Ciphertext &ciph1, const Ciphertext &ciph2, Ciphertext &result, const RelinKeys &relin_key) const;
  • ciph1 (Ciphertext): representing a ciphertext.
  • ciph2 (Ciphertext): representing another ciphertext.
  • result (Ciphertext): storing the computation result.
  • relin_key (RelinKeys): representing the relinearization key.

Usage: multiply_relin computes result = ciph1 * ciph2 and relinearize the ciphertext size of result.


8. Relinearization : relinearize ( only software)

void relinearize(const Ciphertext &ciph, Ciphertext &result, const RelinKeys &relin_keys) const;
  • ciph (Ciphertext): representing a ciphertext.
  • result (Ciphertext): storing the computation result.
  • relin_keys (RelinKeys): representing the relinearization key.

Usage: relinearize function performs relinearization operation on the ciphertext.


9. Ciphertext row rotation : rotate_col

void rotate_col(const Ciphertext &ciph, const GaloisKeys &galois_keys, Ciphertext &result) const override;
  • ciph (Ciphertext): representing a ciphertext.
  • result (Ciphertext): storing the ciphertext after column rotation.
  • galois_keys (GaloisKeys): representing the encryption keys used for row rotation.

Usage: rotate_col performs a column rotation operation on a ciphertext.


10. Ciphertext column rotation : rotate_row

void rotate_row(const Ciphertext &ciph, Ciphertext &result, int step, const GaloisKeys &galois_keys) const;
  • ciph (Ciphertext): representing a ciphertext.
  • result (Ciphertext): storing the ciphertext after row rotation.
  • step (int): An integer representing the rotation step length; a positive value indicates a left rotation while a negative value indicates a right rotation.
  • galois_keys (GaloisKeys): representing the galois keys used for row rotation.

Usage: rotate_row performs a row rotation operation on a ciphertext.


11. Modulo drop: drop_modulus

void drop_modulus(const Ciphertext &ciph, Ciphertext &result, uint32_t level) const;
void drop_modulus_to_next(const Ciphertext &ciph, Ciphertext &result) const;
  • ciph (Ciphertext): representing a ciphertext.

  • result (Ciphertext): storing the ciphertext after dropping the modulus.

  • level (uint32_t): The modulus level to switch into.

Usage: drop_modulus drops the modulus into a specific level. drop_modulus_to_next drops the modulus into the next level.


12. Number Theoretic Transform (forward) : ntt_fwd

void ntt_fwd(const Plaintext &plain, Plaintext &result, parms_id_type parms_id = parms_id_zero) const;
void ntt_fwd(const Ciphertext &ciph, Ciphertext &result) const;
  • plain (Plaintext): representing a plaintext.
  • ciph (Ciphertext): representing a ciphertext.
  • id (Ciphertext): target parms_id of plain(only used in BGV and BFV).
  • result (Ciphertext / Plaintext): store the transformed plaintext or ciphertext.

Usage: ntt_fwd performs the Number Theoretic Transform(NTT) on a plaintext or a ciphertext.


13. Number Theoretic Transform (inverse) : ntt_inv

void ntt_inv(const Ciphertext &ciph, Ciphertext &result) const;
  • ciph (Ciphertext): representing a ciphertext.
  • result (Ciphertext / Plaintext): storing the inverse transformed ciphertext or plaintext.

Usage: ntt_inv performs the Inverse Number Theoretic Transform(INTT) on a plaintext or a ciphertext.


14. Matrix multiplication of ciphertext and plaintext matrix : multiplyByDiagMatrixBSGS

void multiply_by_diag_matrix_bsgs(const Ciphertext &ciph, const MatrixPlain &plain_mat, Ciphertext &result, const GaloisKeys &rot_key) const;
  • ciph (Ciphertext): representing a ciphertext.
  • plain_mat (MatrixPlain): representing a plaintext matrix.
  • result (Ciphertext): storing the computation result.
  • rot_key (GaloisKeys): representing the galois key for rotation.

Usage: multiply_by_diag_matrix_bsgs multiplies a ciphertext with a plaintext matrix, performing the linear transformation over the ciphertext with the Baby-Step-Giant-Step (BSGS) algorithm to accelerate the operations.

The BSGS algorithm can be performed with the following equation.

\begin{aligned} A \cdot z & = \sum\limits_{0 \le j \le N_2} \sum\limits_{0 \le i \le N_1} (u_{N_i \cdot j + i} \odot \rho(z;N_1 \cdot j + i)) \\ & = \sum\limits_{0 \le j < N_2} \rho ( \sum\limits_{0 \le i < N_1} \rho(u_{N_1 \cdot j + i};-N_1 \cdot j) \odot \rho(z;i);N_1 \cdot j ) \end{aligned}

notation:

A denotes the plain matrix

z denotes the ciphertext

N_1 is a divisor of N/2 and N_2 is N/2N_1

\odot denotes the Hadamard (component-wise) multiplication between vectors.

\rho(c;s) denotes the rotation of ciphertext c, the rotation step is s .